Disclamer: I don't know if the mentioned commands are valid for TS-110.

You are correct, if you update UUIDs in /etc/fstab, a 'update-initramfs -u' is required. What you can do is change the UUIDs on the new disk so that they are identical to those of the old disk. Use tune2fs for ext2/3/4 partitions and mkswap for swap partition. I did this on my TS-119 a while back.